Let multidimensional array a with size 3 x 4 be {1,2,3,4,5,6,7,8,9,10,11,12} and b be the last digit of your student number. Accordingly, if we run the given functions in the following order, what will be the output? Explain step by step. function1(b); print(A,b); function2(A,b)B print(A,b); function3(A[b%4][b%3],b); print(A,b);
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b=3 (my number)
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- [Unbalanced Rod] Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure below. -1". /10 2 3 12 2 4 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). where 0 ≤ Pi≤n-1 is the position of weight along the rod. For example, in the figure shown above, the center of mass is computed as C= C = i Wi Pi Σi Wi 10 0+2 1+3·2+4·3+12.4 +2.5 10+2+3+4+12+2 78 33 The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c. Answer the following questions. 1. Describe a greedy algorithm that finds the assignments that…2) Let multidimensional array with size 3 x 4 be a {1,2,3,4,5,6,7,8,9,10,11,12} and b be the last digit of your student number. Accordingly, if we run the given functions in the following order, what will be the output? Explain step by step. b= 5 function1(b); print(A,b); function2(A,b); print(A, b); function3(A[b%4][b%3],b); print(A,b); void print(int a(][3],int b){ printf("\nb=%d",b); for(int i=0;i<4;i++}{ printf("\n"); for(int j=0;j<3;j++}{ printf("%3d",a[i][]); } void function1(int a)}{ a=a+2; void function2(int A[][3],int b){ for(int j=0;j<3;j++){ A[2]]=A[2][i]+b; } void function3(int a,int b){ a=a+b;For this assignment you will be replicating the game of Roshambo (aka rock, paper, scissors). Please answer both parts a and b of the following question below. Show the R code in your answer and annotate all parts of the code. a.) First, you need to come up with a strategy to win the game. Write a function in R that takes in a vector of past plays for your opponent (each play should be represented as "R", "P", or "S") and outputs the next move ("R", "P", or "S"). Your strategy should at least depend on the last two moves used, but you should return a random move if there is not enough past history to use the strategy. b.) Now, play your strategy against a random player who uses rock, paper, or scissors with 1/3 probability each. Who wins the most rounds after 100 rounds of play? Write a function in R.
- A robot moves in a 2D lattice. The robot can only move north (N), south (S), east (E), and west (W) by a certain number of steps. Assume that the robot always starts at (0,0), and that the x axis is oriented east, while the y axis is oriented north. Write a Python function that, given a set of moves, calculates the final position of the robot. For example, if the set of moves provided as input is: N 2 E 4 S 1 W 3 then the final position of the robot is (1,1). The integer that follows a move is always positive. Follow this code skeleton: def robot_move (moves): X = 0 y = 0 # your code here return (x,y) The moves are provided as an array of tuples. The array can have any number of moves in any order. The example above is passed as input as follows: [('N',2), ('E',4), ('S',1), ('W',3)]1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 16Your checkWinner function should determine whether or not the game is over. If the game is over, it should print who won (if anyone), and return true. If the game is not over, it should return false. The game is over if someone wins by getting three X's or three O's in a row, column or diagonal. So there are 8 different combinations of 3-in-a-row moves. You may assume that the board has a size of 3 (length and width). The TicTacBoard.java file I'm giving you uses a variable for that size, but you can assume it's always 3. The game is also over if the board is full but nobody won. I recommend you write some other functions to help in determining if the game is over. Remember you should never copy and paste code if you can avoid it. Write a function to perform a common, generalizable task, and call that function every time you need it. (Like I did with my dispRow method.) Please follow the standard conventions for indentation, meaningful variable names, etc. like the examples in class…
- Your checkWinner function should determine whether or not the game is over. If the game is over, it should print who won (if anyone), and return true. If the game is not over, it should return false. The game is over if someone wins by getting three X's or three O's in a row, column or diagonal. So there are 8 different combinations of 3-in-a-row moves. You may assume that the board has a size of 3 (length and width). The TicTacBoard.java file I'm giving you uses a variable for that size, but you can assume it's always 3. The game is also over if the board is full but nobody won. I recommend you write some other functions to help in determining if the game is over. Remember you should never copy and paste code if you can avoid it. Write a function to perform a common, generalizable task, and call that function every time you need it. (Like I did with my dispRow method.) Please follow the standard conventions for indentation, meaningful variable names, etc. like the examples in class…There is a large pile of socks that must be paired by color. Given an array of integers representing the color of each sock, determine how many pairs of socks with matching colors there are. Example There is one pair of color and one of color . There are three odd socks left, one of each color. The number of pairs is . Function Description Complete the sockMerchant function in the editor below. sockMerchant has the following parameter(s): int n: the number of socks in the pile int ar[n]: the colors of each sock Returns int: the number of pairs Input Format The first line contains an integer , the number of socks represented in .The second line contains space-separated integers, , the colors of the socks in the pile. Constraints where Sample Input STDIN Function ----- -------- 9 n = 9 10 20 20 10 10 30 50 10 20 ar = [10, 20, 20, 10, 10, 30, 50, 10, 20] Sample Output 3 Explanation There are three pairs of socks.1. Write a function (call it mylm) that takes two inputs: a vector y of n elements and a matrix X of n times k elements, where n should be greater than k, and returns three outputs: bhat = solve(X'X)X'y, X'X and X'y (the prime symbol means transpose). Use the attr method to return the second and third outputs. Note that you do not need to specify values for y and X when you write this function.
- There is a large pile of socks that must be paired by color. Given an array of integers representing the color of each sock, determine how many pairs of socks with matching colors there are. Example There is one pair of color and one of color . There are three odd socks left, one of each color. The number of pairs is . Function Description Complete the sockMerchant function in the editor below. sockMerchant has the following parameter(s): int n: the number of socks in the pile int ar[n]: the colors of each sock Returns int: the number of pairs Input Format The first line contains an integer , the number of socks represented in .The second line contains space-separated integers, , the colors of the socks in the pile. Constraints where Sample Input STDIN Function ----- -------- 9 n = 9 10 20 20 10 10 30 50 10 20 ar = [10, 20, 20, 10, 10, 30, 50, 10, 20] Sample Output 3) Let O be the set of odd numbers and O’ = {1, 5, 9, 13, 17, ...} be its subset. Definethe bijections, f and g as:f : O 6 O’, f(d) = 2d - 1, d 0 O.g : ø 6 O, g(n) = 2n + 1, n 0 ø.Using only the concept of function composition, can there be a bijective map from øto O’? If so, compute it. If not, explain in details why not...................................................................................................................................... [2+8]b) A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W,X, Y and Z.We define the relation: A Sesotho word x is related to another Sesotho word y if xbegins with the same letter as y.Determine whether or not this is an equivalence relation.If it is an equivalence relation then1. Compute C(sekatana)2. How many equivalence classes are there in all, and why?3. What is the partition of the English words under this relation?If it is NOT an equivalence relation then explain in details why it is notTrue or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).